9*. The sequence $a_1, a_2, a_3, a_4, a_5, a_6, a_7$ is an increasing geometric sequence in which each term is an
integral power of 3. Also,
$\log_3(a_1) + \log_3(a_2) + \log_3(a_3) + \log_3(a_4) + \log_3(a_5) + \log_3(a_6) + \log_3(a_7) = 322$
and
$61 \le \log_3(a_1 + a_2 + a_3 + a_4 + a_5 + a_6 + a_7) \le 62$
Determine the value of $a_1$.